Question

Witch of the following was not a motive for imperialism in the nineteenth century? To expand the territory of western nations.

Answer 1

To offer medical assistance to Third World countries.

The imperialism movement of the 19th century did not show particular concern for the native peoples in the regions they came to control through imperialistic means.  There were medical missions and religious missions that accompanied the imperialistic advance into other countries, but those were factors that accompanied the imperialistic advance more than they motivated it.  
Also, as a false component of that option, the term "Third World" didn't come into existence until the era of the Cold War.  The "Third World" referred to the developing nations that did not align with either of the superpowers, the USA or the USSR.   No one was using the term "Third World" in the 19th century.